NEW YORK, Nov 24 (Reuters) - Wells Fargo & Co has asked a U.S. court to order dozens of customers who are suing the bank over the opening of unauthorized accounts to resolve their disputes in private arbitrations instead of court, according to legal documents.

The motion, filed in the U.S. District Court in Utah on Wednesday, is in response to the first class action lawsuit filed against Wells since it agreed to pay $185 million in penalties and $5 million to customers for opening up to 2 million deposit and credit-card accounts in their names without their permission.

The scandal has shaken Wells, the third-largest U.S. bank by assets. Its former Chief Executive Officer John Stumpf stepped down amid the furor, it has been put under tougher regulatory scrutiny and its reputation has been damaged as it faces multiple probes.

The move to enforce the mandatory arbitration clauses comes as Wells Fargo has launched an advertising campaign to win back customer loyalty in the wake of the scandal.

"We are saddened that despite Wells Fargo's commercials and promises to make things right, Wells Fargo is choosing to harm their customers once more," said Zane Christensen, the plaintiffs' lawyer in Sandy, Utah, in a statement.

A spokesman for Wells Fargo declined to comment on the filing.

In a written response to questions from U.S. lawmakers, published last week, the bank said it would stand by its arbitration policy but was offering free mediation services to affected customers.

Mandating arbitration when signing up for financial products has become standard practice after a 2011 U.S. Supreme Court decision validated the practice. But customer advocates say it improperly denies customers the legal protections of court proceedings, such as the right to appeal, and helps to conceal corporate misconduct from the public and regulators because documents and hearings are not made public.

Customers trying to recover small sums of money are also unlikely to find lawyers to represent them in arbitration, critics say, and the cases do not set a legal precedent to help other affected individuals.

Last year, a court dismissed an earlier lawsuit against Wells Fargo, saying that customers had signed arbitration clauses when opening their accounts.

The bank has come under fire over its mandatory arbitration clauses from Democratic lawmakers in Congress, including Senator Elizabeth Warren of Massachusetts. (Editing by Carmel Crimmins and Marguerita Choy)